All good advice above.
Had a Rega for many years before I got my Sota. Yours will need the oil changed, not added. It's easy to do, but a bit messy. You'll have to gently pull up on the spindle assembly against the vacuum seal the oil will create while rotating it until it comes free. Then use swabs to clean out the old oil and invert the table to remove the ball bearing. Clean the well and bearing with denatured alcohol (be careful not to get any on any non-metallic surfaces) and let it all dry. Inspect the bearing to make sure it's not pitted. Then reverse the process with a really good synthetic turntable oil (Needle Doctor is one source that has several to choose from). Be patient! You want to make sure you don't get any air bubbles trapped between the spindle assembly shaft and the bearing.
Definitely replace the belt. Cheap, easy and will make a world of difference on spin up and torque retention. Clean the belt pulley and the spindle assembly surface with 91% rubbing alcohol and allow to air dry thoroughly. Do not get any on the belt itself; the new belt will have a dressing on it that you want to keep intact. Inspect the O-rings that suspend the motor carefully. If they appear cracked or are brittle (they probably are), change them out. Use compressed air to blow the dust of ages out of the motor, then lubricate the bearing surfaces where the armature spindle exits cautiously.
The stylus assembly on the cartridge is almost certainly toast. The magnets in MM carts get weak with age, and yours is almost certainly below optimum strength now. Buy a new one or get a new cartridge altogether. Note that MC carts don't suffer from this particular problem as the magnets are much bigger.
Look very carefully at the RCA leads. If the jackets are cracked and/or the jacks themselves are corroded, you will have to evaluate the relative merits of a restoration job against just replacing them. 24 years is a long time, and copper oxidizes even under vinyl jackets. If the oxidization is too extensive, a complete headshell to jack rewire or arm replacement might be necessary. Remember, the arm has bearings too. The oil in them also oxidizes and that affects the ability of the arm to track without excessive friction.
Next, buy a damn good protractor if you don't already have one, new cartridge leads, a powerful illuminated bench magnifier and a case of beer. Take your time, install the new leads and do a hyper-precise cartridge alignment. The RB 300 on the Planar 3 is tricky to get just right, so you will want a beer or two to steady your hand while you're doing it. After you've spent the next 3 hours getting it perfect, turn out the light on the bench mag, drink the rest of the beer and go to bed.
Last, plug it all back into your system and do some auditioning. You won't be disappointed. Good luck & happy listening!